Entropy rigidity for 3D conservative Anosov flows and dispersing billiards - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Geometric And Functional Analysis Année : 2020

Entropy rigidity for 3D conservative Anosov flows and dispersing billiards

(1) , (2) , ,
1
2

Résumé

Given an integer k >= 5, and a C-k Anosov flow F on some compact connected 3-manifold preserving a smooth volume, we show that the measure of maximal entropy is the volume measure if and only if Phi is Ck-epsilon-conjugate to an algebraic flow, for epsilon > 0 arbitrarily small. Moreover, in the case of dispersing billiards, we show that if the measure of maximal entropy is the volume measure, then the Birkhoff Normal Form of regular periodic orbits with a homoclinic intersection is linear.

Dates et versions

hal-03622085 , version 1 (28-03-2022)

Identifiants

Citer

Jacopo de Simoi, Martin Leguil, Kurt Vinhage, Yun Yang. Entropy rigidity for 3D conservative Anosov flows and dispersing billiards. Geometric And Functional Analysis, 2020, 30 (5), pp.1337-1369. ⟨10.1007/s00039-020-00547-z⟩. ⟨hal-03622085⟩
4 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook Twitter LinkedIn More